Blood oxygen level-dependent (BOLD) MRI is a non-invasive diagnostic method for assessing tissue oxygenation level, by changes in the transverse relaxation time T2*. 3D BOLD imaging of lung tumours is challenging, because respiratory motion can lead to significant image quality degradation. The purpose of this work was to explore the feasibility of a three dimensional (3D) Cartesian multi gradient echo (MGRE) sequence for T2* measurements of non-small cell lung tumours during free-breathing. A non-uniform quasi-random reordering of the pahse encoding lines that allocates more sampling points near the k-space origin resulting in efficient undersampling pattern for parallel imaging was combined with multi echo acquisition and self-gating. In a series of three patients 3D T2* maps of lung carcinomas were generated with isotropic spatial resolution and full tumour coverage at air inhalation and after hyperoxic gas challenge in arbitrary respiratory phases using the proposed self-gated MGRE acquisition. The changes in T2* on the inhalation of hyperoxic gas relative to air were quantified. Significant changes in T2* were observed following oxygen inhalation in the tumour (p < 0.02). Thus, the self-gated MGRE sequence can be used for assessment of BOLD signal with isotropic resolution and arbitrary respiratory phases in non-small cell lung cancer.Copyright © 2020 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.